Stabilization of T–S fuzzy membership-function dependent H $$_\infty $$ -based sampled-data control systems using an improved exponential two-sided looped-functional approach

Abstract

This study concerns the exponential stability and stabilization problem for the Takagi–Sugeno (T–S) fuzzy systems under the membership function dependent (MFD) H\(_\infty \)-based sampled-data control (SDC) using an improved exponential two-sided looped-functional (TSLF) approach. First, an exponential TSLF is introduced to achieve the state information within the intervals \(t_{\textrm{k}}\) to t and t to \(t_{\textrm{k}+1}\), which not only relaxes the monotonic constraint but would also not impose the terms as positive definite. By employing the concept of looped-functional, a new exponential TSLF is introducing the exponents \(e^{2\alpha (t-t_{\textrm{k}})},\) \(\frac{e^{2\alpha (t_{\textrm{k}+1}-t)}-1}{2\alpha }\), and \(\frac{e^{-2\alpha (t-t_{\textrm{k}})}-1}{2\alpha }\), thereby enhancing the control performance, design flexibility and also it contains the more actual sampling information of system states. Next, the new exponentially stable lemma is derived from the fuzzy SDC system with an external disturbance. To this end, the time derivatives of exponential TSLF-based Lyapunov–Krasovskii functional, some stabilization criteria exist in formulating linear matrix inequalities to secure the system is exponentially stable under MFD H\(_\infty \) criterion. Finally, the chaotic permanent magnet synchronous generator-based wind energy system is demonstrated under the practical values with proposed sufficient conditions, and Rossler’s model expresses the advantages and excellence of the proposed techniques.